Consider a resonator with ω0 = 100 rad/sec and a Q factor of 100. Calculate the time takes it to settle within 2% of the final value when ex

Question

Consider a resonator with ω0 = 100 rad/sec and a Q factor of 100. Calculate the time takes it to settle within 2% of the final value when excited with a unit force.

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Gia Bảo 3 years 2021-09-05T14:55:27+00:00 1 Answers 33 views 0

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  1. thanhcong
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    2021-09-05T14:57:06+00:00
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    Answer:

    8 s

    Explanation:

    Damping factor, F is given by

    F=\frac {1}{2Q} where Q is quality factor

    Also, we know that the settling time, T is given by

    T=\frac {4}{FW} where W is the resonant frequency.and substituting the first equation here we get

    T= \frac {4\times 2Q}{W}

    Since it takes 2% of final value to settle and considering 100 rad/s for resonant frequency and taking quality factor of 100 then  

    T=\frac {4\times 2\times 100}{100}= 8 s

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